A rack steering gear is known, for example, from German Offenlegungsschrift No. 2,001,478. The cylindrical plastic thrust piece contained in such steering mechanism is made hollow and is mounted in the rack housing with a relatively thick-walled guide part. The guide part is supported on its side remote from the rack against a sheet-metal ring deformed during assembly. Due to the bracing of the thrust piece between the sheet-metal ring and the rack, an elasticity is provided which is sufficient, in the new state, to press the rack against the drive pinion. However, after a certain operating time the thrust-piece bedding for the rack can wear away, so that play arises between the bedding and the rack. A sufficient dampening of rack vibration then seems to be no longer guaranteed. Since plastics are inclined to swell under the influence of temperature and atmospheric moisture, that is to say they increase their volume, too large a radial compression in the housing bore can arise on the guide part of the thrust piece. This leads to the occurrence of jamming. If, on the contrary, the play is chosen too large, the thrust piece can rattle due to radial movements.
It is also known from German Utility Model G 71 37 869.3 to insert an elastic ring into an annular groove on the outer periphery of the thrust piece in order to dampen the lifting movements of the thrust piece. However, here, the thrust piece itself is made entirely of rigid metal.